$ \left(\dfrac{1}{16}\right)^{\frac{7}{4}}$
Explanation: $= \left(\left(\dfrac{1}{16}\right)^{\frac{1}{4}}\right)^{7}$ To simplify $\left(\dfrac{1}{16}\right)^{\frac{1}{4}}$ , figure out what goes in the blank: $\left(? \right)^{4}=\dfrac{1}{16}$ To simplify $\left(\dfrac{1}{16}\right)^{\frac{1}{4}}$ , figure out what goes in the blank: $\left({\dfrac{1}{2}}\right)^{4}=\dfrac{1}{16}$ so $ \left(\dfrac{1}{16}\right)^{\frac{1}{4}}=\dfrac{1}{2}$ So $\left(\dfrac{1}{16}\right)^{\frac{7}{4}}=\left(\left(\dfrac{1}{16}\right)^{\frac{1}{4}}\right)^{7}=\left(\dfrac{1}{2}\right)^{7}$ $= \left(\dfrac{1}{2}\right)\cdot\left(\dfrac{1}{2}\right)\cdot \left(\dfrac{1}{2}\right)\cdot \left(\dfrac{1}{2}\right)\cdot \left(\dfrac{1}{2}\right)\cdot \left(\dfrac{1}{2}\right)\cdot \left(\dfrac{1}{2}\right)$ $= \dfrac{1}{4}\cdot\left(\dfrac{1}{2}\right)\cdot \left(\dfrac{1}{2}\right)\cdot \left(\dfrac{1}{2}\right)\cdot \left(\dfrac{1}{2}\right)\cdot \left(\dfrac{1}{2}\right)$ $= \dfrac{1}{8}\cdot\left(\dfrac{1}{2}\right)\cdot \left(\dfrac{1}{2}\right)\cdot \left(\dfrac{1}{2}\right)\cdot \left(\dfrac{1}{2}\right)$ $= \dfrac{1}{16}\cdot\left(\dfrac{1}{2}\right)\cdot \left(\dfrac{1}{2}\right)\cdot \left(\dfrac{1}{2}\right)$ $= \dfrac{1}{32}\cdot\left(\dfrac{1}{2}\right)\cdot \left(\dfrac{1}{2}\right)$ $= \dfrac{1}{64}\cdot\left(\dfrac{1}{2}\right)$ $= \dfrac{1}{128}$